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Schrodinger time dependent wave equation derivation

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Schrodinger time independent wave equation derivation

Schrodinger time dependent wave equation derivation

Consider a particle of mass “m” with velocity “v” and under the influence of potential energy (P.E) which is represented by V(r) .The total energy of the particle is the sum of potential energy (P.E) and kinetic energy (K.E) which is given by:

schrodinger wave equation derivation

schrodinger wave equation

schrodinger wave equation

 

schrodinger wave equation

time dependent schrodinger wave equation

 

 

schrodinger time dependent wave equation formula

This is the schrodinger time dependent wave equation formula.

The factor hamiltonian operator formula=H is known as Hamiltonian operator which gives the energy of the particle.Now equation (7) can be written as:

time dependent schrodinger wave equation in general form

 

 

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